The present invention relates to a position calibrating method for a measuring apparatus structured in such a manner that a plurality of optical length measuring devices are provided.
When calibrating a position of a contact detector in a three-dimensional coordinate measuring device, a master ball has been generally used. The master ball has good sphericity whose diameter is calibrated with a high accuracy. Specifically, three or more points on a surface of the master ball are measured by the contact detector and an arithmetic operation is performed based on these surface coordinates to calculate a central coordinate of the master ball. The thus-obtained central coordinate of the master ball is used as a reference coordinate to effect position calibration of the measurement data when actually measuring a workpiece.
However, when using an optical length measuring device (for example, an image measuring head using a CCD or a laser displacement gauge which is a non-contact detector), a point on an inclined surface must be measured when attempting calibration by using the same technique employing the master ball as in the case of using the contact detector. An error will be included in measurement of the vertical axis (Z-axis) coordinate value of that point because the light is not reflected on the inclined (curved) surface in the vertical axis direction when irradiating the light from the vertical axis direction. This error adversely affects a result of the arithmetic operation of the master ball central coordinate value and leads to another serious error in the Z and Y coordinate values of the obtained central coordinate value. Further, the usual optical length measuring device cannot bring the inclined surface into focus, and hence the measuring point must be selected only from an extremely small area, which also causes an arithmetic operation error.
The specific description will be given as to the influence of an error in the Z-axis coordinate value at a given measured point on the central coordinate value to be obtained when calculating the central coordinate value from coordinate values of four measuring points on the surface of the master ball. The master ball has a diameter R as shown in FIG. 6 and its spherical surface can be represented by the following Expression 1 with its origin in the center.
Expression 1 EQU x.sup.2 +y.sup.2 +z.sup.2 =R.sup.2
Assuming that the central coordinate of the master ball is (a, b, c), the spherical surface can be represented by the following Expression 2.
Expression 2 EQU (x-a).sup.2 +(y-b).sup.2 +(z -c).sup.2 =R.sup.2
The central coordinate is obtained by measuring four points on a surface of such a master ball, i.e., a position of an intersection with the Z-axis P1 (0, 0, R) and three surface positions selected from the circumference of the point P1 and each having an angle .theta. inclined from the z-axis P2 (Rsin.theta., 0, Rcos.theta.), P3 (0, Rsin.theta., Rcos.theta.) and P4 (Rsin.theta., 0, Rcos.theta.). It is assumed that P1, P2 and P4 in the above respective data are accurately measured and an error .delta. is included in the z coordinate value in the coordinate of the measured point P3, which results in P3 (0, Rsin.theta., Rcos.theta.+.delta.). Here, the operation formula for calculating the central coordinate value (a, b, c) of the master ball can be represented by the following Expression 3 by substituting for measured data at points P1, P2, P3 and P4 in Expression 2.
Expression 3 EQU a.sup.2 +b.sup.2 +(R-c).sup.2 =R.sup.2 (1) EQU (R sin.theta.-a).sup.2 +b.sup.2 +(R cos.theta.-c).sup.2 =R.sup.2(2) EQU a.sup.2 +(R sin.theta.-b).sup.2 +(R cos.theta.-c+.delta.).sup.2 =R.sup.2(3) EQU (Rsin.theta.+a).sup.2 +b.sup.2 +(R cos.theta.-c).sup.2 =R.sup.2(4)
The X coordinate value a can be obtained as shown by the following Expression 4 by subtracting the formula (2) and the formula (4) in Expression 3.
Expression 4 EQU 4Rasin.theta.=0 EQU .thrfore.a=0
By substituting a=0 in the formulas (1), (2) and (3), (1'), (2') and (3') shown by the following Expression 5 can be obtained.
Expression 5 EQU b.sup.2 +(R-c).sup.2 =R.sup.2 (1') EQU (R sin.theta.).sup.2 +b.sup.2 +(R cos.theta.-c).sup.2 =R.sup.2(2') EQU (R sin.theta.-b).sup.2 +(R cos.theta.-c+.delta.).sup.2 =R.sup.2(3')
The Z coordinate value c can be obtained as shown by the following Expression 6 by subtracting the formulas (1') and (2').
Expression 6 EQU 2Rc(cos.theta.-1)=0 EQU .thrfore.c=0
When substituting c=0 in the formulas (2') and (3') and subtracting them, the Y coordinate value b can be obtained as shown by the following Expression 7.
Expression 7 EQU b=(.delta..sup.2 +2R.delta. cos.theta.)/2R sin.theta.
In this way, if an error is included in the z coordinate value measured with respect to the measured point P3 whose Y coordinate value is not 0, an error is included in the Y coordinate value of the central coordinate value to be obtained. Similarly, if there is an error in the z coordinate value when measuring the point P2 or P4 whose X coordinate value is not 0, an error is included in the x coordinate value of the central coordinate value to be obtained.
As described above, when adopting the optical length measuring device and trying position calibration by using the master ball, there occurs such a problem as that the central coordinate value of the master ball, i.e., the position data for calibration cannot be accurately obtained due to the influence of the error in measurement of the vertical axis coordinate value. Further, since the optical length measuring device cannot bring the inclined (curved) surface into focus, the measuring point is disadvantageously restricted in a small area, which makes it difficult to obtain the accurate calibration data.